Location of an autonomous driving vehicle (ADV) is determined with respect to a high definition map. On-boards sensors of the ADV obtain a 3D point cloud of objects surrounding the ADV. The 3D point cloud is organized into an ADV feature space of cells. Each cell has a median intensity value and a variance in elevation. A set of candidate cells that surround the ADV is determined. For each candidate, a set of cells of the ADV feature space that surround the candidate cell is projected onto the map feature space using kernel projection, for one or more dimensions. Kernels can be Walsh-Hadamard vectors. Candidates having insufficient similarity are rejected. When a threshold number of non-rejected candidates remain, candidate similarity can be determined using a similarity metric. The coordinates of the most similar candidate cell are used to determine the position of the vehicle with respect to the map.